Without knowing anything about your file nobody can say much, but not to shatter your illusions: You will probably have to live with it. When enabling the rasterizing for the unsupported features, you get an embedded JPEG sequence in the SWF and the files become large. If you choose to not rasterize, then only supported vector features will come over. Either way, the workflow is unsuitable and not up to modern standards. You'd do better rendering a H.264 clip or similar.
What would you like to know about the file?
AE is about the worst app for producing a SWF file there ever was. It will convert almost all effects to raster images which makes the file size balloon. If you want to produce SWF's for the web that meet data size and data rate specifications you'll need to learn how to use flash or embed movies in your SWF's inside flash.
As the others say, do this:
Create an H.264 video file and then use Flash Professional to embed or link that video file into a SWF container file.
Do not create SWF files from After Effects.